Fuzzy Superpixel Segmentation with Anisotropic Total Variation Regularization

This paper presents a superpixel segmentation algorithm that integrates anisotropic total variation regularization within a fuzzy clustering framework. While isotropic total variation is well-known for its edge-preserving properties, its non-adaptive nature often leads to over-regularization. In contrast, the anisotropic model formulates superpixel regularity in relation to image contours, thereby preventing the loss of image details in areas of high contour density during optimization. Compared to classical segmentation algorithms that employ non-adaptive regularization, the proposed content-adaptive approach enhances superpixel regularity while maintaining boundary adherence to image contours. Furthermore, to optimize the functional effectively, an alternating direction method of multipliers along with the enhanced Chambolle’s fast duality projection algorithm are employed. Competitive experiments against existing regular segmentation algorithms demonstrate that our proposed methodology achieves superior performance in terms of boundary recall, compactness, and shape regularity criteria, outperforming these methods by an average of at least 3%, 5%, and 3%, respectively. Furthermore, when compared with irregular segmentation algorithms, our approach achieves the best results in terms of compactness, contour density, and shape regularity criteria, with average improvements of at least 56%, 22%, and 45%, respectively.